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24 Cracking From Case P1 Total Cracking After Case P1 Figure 29. 4GHFNON Case P1 cracking. especially at the ultimate limit state. Local behavior (i.e., f. That the web flexural buckling was observed pro- slippage and separation of the concrete deck from the vides additional confirmation that the neutral axis had steel girder), however, would normally be used to clas- moved up--consistent with a full effective width. sify the girder as noncomposite. 5. Despite the problems encountered with deck gages Thus, the principal insights from the experiments were that a. There was good correlation of deck strains with FEM the FEM methodology employed was reasonably trustworthy strains before cracking, for extracting effective width and that full width is consistent b. Overall load-deflection prediction was good, with those experimental results. Further details on the exper- c. Existence and extent of cracking was reasonably well iments conducted are provided in Appendixes E and F. predicted by the smeared cracking approach used in the FEM herein, d. Steel strains correlated well with FEM predictions 2.4 FEM PARAMETRIC STUDY pre-buckling, e. Those strain profiles confirmed the upward move- In the parametric study of the effective slab width proj- ment of the neutral axis consistent with the full effec- ect (NCHRP Project 12-58), design of experiment (DOE) tive width predicted by FEM for the experiment, and concepts described in Appendix G were employed to ensure

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25 (in) 0 1 2 3 4 5 6 7 8 9 10 450 100 400 90 350 80 70 300 0.95Py FEM 60 Force (kN) 250 4GHFNON (kips) 50 LG 200 4GHFCOM 40 150 0.50Py 30 100 20 50 10 0.95Pcr 0 0 0 50 100 150 200 250 Displacement (mm) Figure 30. Comparative force versus displacement at 1.20L. that both common and extreme cases were covered. In addi- were calculated using the QConBridge software. Bridges tion, curve-fitted equations were derived considering the were designed for these load effects using MathCad Work- effects from each parameter. Various cases were considered: sheets developed for that purpose. Bridges so designed were checked using the OPIS 5.0 software. Line girder analysis Simple-span right bridge (non-skewed), with the current 12t-limited effective slab width was used for Simple-span with skewed supports, each of the designs. Details of deck and girder design con- Multiple-span continuous right bridge (non-skewed), and siderations are summarized below. Multiple-span continuous with skewed supports. 2.4.1.1 Deck Design By using DOE, all cases for both simple-span and multiple- span continuous bridges are illustrated in Tables 3 and 4, The thinnest practicable deck was used in order to maxi- respectively. mize shear lag behavior. The deck thickness depended on the For simple-span cases, the main parameters are girder spacing. The following thicknesses were used: Girder spacing (S) 2.4 m to 4.8 m, Girder Deck Span length (L) from 15 m to 60 m, and Spacing Thickness S/t Design Method Skew angle () from 0 degree to 60 degrees. 2.4m 175mm 13.7 Empirical Design For multiple-span continuous cases, the main parame- 3.6m 200mm 18.0 Empirical Design ters are 4.8m 240mm 20.0 Conventional Girder spacing (S) 2.4 m to 4.8 m, Overhang width was assumed as 0.4S for every bridge Exterior span length (L1) from 20 m to 60 m, design based on an investigation of overhang width on several Interior-to-exterior span ratio (L2 /L1) from 1 to 1.5, and bridges to produce the same exterior girder as used for the Skew angle () from 0 degree to 60 degrees. interior girder, with similar structural efficiency, i.e., perfor- mance ratio. 2.4.1 Bridge Designs for Parametric Study Skewed Deck. Two skew angles were considered in the designs: 30 and 60 degrees. The reinforcement in both All bridges in the parametric study were designed accord- directions was doubled in the end zones of the deck and ing to a common set of industry guidelines for economical placed perpendicular to the main supporting components as design of slab-on-steel girder-type structures. These guide- specified in Article 9.7 of the AASHTO LRFD code. lines are as follows. Strength I, Service II, and Fatigue and Fracture limit states Negative Moment Regions. The total cross-sectional area were considered in the designs, as was the construction stage of the longitudinal reinforcement should not be less than assuming conventional unshored construction. Load effects 1 percent of the total cross-sectional area of the slab. The

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26 Girder 2 Deflection at 0.95Pcr (in) 0 50 100 150 200 250 25 1 0 0 Deflection (mm) -25 -1 (in) -50 -2 -75 -3 4GHFCOM 4GHFNON LG FEM -100 -4 0 1000 2000 3000 4000 5000 6000 7000 Longitudinal Distance (m m ) Girder 2 Deflection at 0.50Py (in) 0 50 100 150 200 250 25 1 0 0 Deflection (mm) -25 -1 (in) -50 -2 -75 -3 4GHFCOM 4GHFNON LG FEM -100 -4 0 1000 2000 3000 4000 5000 6000 7000 Longitudinal Distance (m m ) Girder 2 Deflection at 0.95Py (in) 0 50 100 150 200 250 25 1 0 0 Deflection (mm) -25 -1 (in) -50 -2 -75 -3 4GHFCOM 4GHFNON LG FEM -100 -4 0 1000 2000 3000 4000 5000 6000 7000 Longitudinal Distance (m m ) 0.70L 0.80L 0.90L 0.95L 1.00L 1.05L 1.10L 1.20L 1.30L 0.75L 1.25L Figure 31. Comparative deflection profiles. minimum yield strength of reinforcement should not be less 2.4.1.2 Girder Design than 420 MPa and a size not exceeding #19 (metric, #6 Eng- lish) bars. Guidelines employed for the girder design included the Prestressed deck should be considered when S/t 20, which following: corresponds to the 4.8 m girder spacing. Prestressed deck was not considered as part of the basic parametric study but The minimum web plate thickness was assumed as was considered as one of the special cases. 11 mm.

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27 TABLE 3 Simple-span parametric study cases Bridge ID Parameter L/S S (m) L (m) (degrees) SS-01 2.4 15 0 6.25 SS-03 4.8 15 0 3.125 SS-07 2.4 60 0 25 SS-09 4.8 60 0 12.5 SS-19 2.4 15 60 6.25 SS-21 4.8 15 60 3.125 SS-25 2.4 60 60 25 SS-27 4.8 60 60 12.5 TABLE 4 Multiple-span continuous parametric study cases Bridge ID Parameter L1/S S (m) L1 (m) L2/L1 (degrees) CS-01 2.4 20 1.0 0 8.33 CS-03 4.8 20 1.0 0 4.17 CS-07 2.4 60 1.0 0 25 CS-09 4.8 60 1.0 0 12.5 CS-19 2.4 20 1.5 0 8.33 CS-21 4.8 20 1.5 0 4.17 CS-25 2.4 60 1.5 0 25 CS-27 4.8 60 1.5 0 12.5 CS-55 2.4 20 1.0 60 8.33 CS-57 4.8 20 1.0 60 4.17 CS-61 2.4 60 1.0 60 25 CS-63 4.8 60 1.0 60 12.5 CS-73 2.4 20 1.5 60 8.33 CS-75 4.8 20 1.5 60 4.17 CS-79 2.4 60 1.5 60 25 CS-81 4.8 60 1.5 60 12.5 The minimum flange size was assumed as 19 mm investigated in such cases, but those considerations were 300 mm. not the focus of the present study. The Traditional Minimum Depth requirement was For shear in skewed bridges, the same web thickness applied [AASHTO LRFD Table 2.5.2.6.3-1]. was used for both right and skewed bridges sharing the Uniform depth was assumed for web design throughout same span lengths and girder spacings to avoid devia- the length of a bridge. tion of flexural effects if possible. Shear effects in any The web was designed as partially stiffened, if applicable. two such comparable bridges are not the same, however, For simply supported girders, girder transitions were because of the shear correction applied to the distribu- located at 0.2L and 0.8L. For continuous girders, girder tion factor for skewed bridges. transitions were located approximately at 0.7L, 1.2L, 1.8L, and 2.3L. More details on the specifics of the industry guidelines and The top flange width was fixed for every design; heav- rules of thumb used to design the suite of bridges in the para- ier flange requirements were accommodated by varying metric study set, along with resulting girder section sizes and thickness. The bottom flange width was changed only in governing limit states, are provided in Appendix H. negative moment regions. For positive moment regions, most of the girder sections 2.4.2 Simple-Span Bridges were compact. For negative moment regions, noncom- pact sections (noncompact web) were used if applicable. Finite element analyses of eight simple-span bridge con- Designs were fine-tuned to have the maximum perfor- figurations were conducted using the general-purpose finite mance ratio for the most critical limit state exceed 95 per- element analysis software, ABAQUS. Configurations of all cent (except in some cases where the aforementioned simple-span bridges are illustrated in Table 3. Bridges ranged minimum flange size of 19 mm 300 mm was used). from 15 to 60 m in span length, 2.4 to 4.8 m in girder spac- For skewed bridges, intermediate cross frames were ing, and 0 to 60 degrees in skew angle at the supports. Most oriented normal to the main members. Cross frames bridges were designed to have two flange transition points at may be staggered or discontinuous across the bridge. 0.2L and 0.8L, where L is the span length. Material proper- Displacement-induced fatigue considerations should be ties are summarized in Table 5.

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28 TABLE 5 Material properties for parametric study and were connected by straight lines. The series of numbers cases after the bridge ID contain the bridge configuration informa- Material Description Value tion. The three numbers are Steel Elastic modulus, Es 200 GPa Girder spacing (m), Yield strength, Fy 345 MPa Concrete Elastic modulus, Ec 24.4 GPa Span length (m), and Compressive strength, f 'c 28 MPa Skew angle (degree). Reinforcement Elastic modulus, Erebar 200 GPa Yield strength, fy 420 MPa Shear Connector Elastic modulus, Esc 200 GPa Thus, for bridge SS-19: 2.4/15/60 represents a bridge with Yield strength, fy,sc 345 MPa 2.4-m-girder spacing, 15 m long, and 60-deg skew angle. Ultimate strength, fu,sc 420 MPa Truck placement location is indicated in the diagram of each plot of beff /b. The results show that a full slab width can be used as the All bridges were subjected to the nominal live load, which effective slab width for all investigated right bridges. These consists of HL-93 trucks and lane load, including impact encompass a L/S range of 3.125 to 25. effects. Both truck and lane loads were applied at the specific The SS-07 bridge has the highest L/S value among the four location to simulate the maximum positive moment condi- right bridges, hence the most flexural dominated structural tion. Longitudinally, the middle axle of the truck was located behavior. Likewise, SS-09, with the second highest L/S value, at mid-span of the bridge, while the trucks were placed trans- exhibits similar behavior with the beff /b of 1.0 across the versely across the width to maximize the bending moment in either interior or exterior girders, whichever was the focus entire span length. of interest. In the region close to the abutments, the support boundary Each simple-span bridge analysis can be subdivided into conditions influenced the effective slab width ratio. The closer two categories at the Service II limit state: the section was to the end support, the smaller the effective slab width ratio tended to be. In most practical situations, there Interior girder, and is significant excess flexural capacity as well near end sup- Exterior girder. ports. Thus the reduction in beff /b should not be of concern in such regions. The support effect becomes more prominent as Truck configurations are illustrated in Figure 32 for the the L/S values get smaller. For instance, the interior girder interior girder loading and Figure 33 for the exterior girder effective slab width ratios of the SS-03 bridge reduced below loading. Distances between the front-to-middle axles and 1.0 further away from the supports than SS-01. rear-to-middle axles were chosen to have the minimum of For the interior girder and highly skewed cases, three out 4.3 m based on the code and the influence line principle for of four bridges exhibited an effective slab width ratio of less simple-spans. Additionally, lane load configurations are illus- than 1.0. The exception was the SS-25 bridge, which had a trated in Figures 34 and 35 for the interior girder and exterior high L/S of 25 (see Figure 36). But where beff /b < 1 near girder loading, respectively. For the purpose of the paramet- midspan, the bending moment diagrams of short-span skewed ric study, all bridges were analyzed up to the serviceability bridges SS-19 and SS-21 extracted from FEM do not have limit state (SERVICE II), which has the load combination of the shape or magnitude used in the girder design based on 1.0(DC1 & DC2 & DW) + 1.3(LL & IM). A limited number line girder analysis. FEM-extracted moments in these bridges, of Strength limit state cases were chosen randomly to verify as shown in Figure 36, were less than the moments that full that the serviceability limit states always governed the effec- truck axle loads produce in a line-girder analysis. tive slab width values. Table 7 compares the extreme fiber stresses with Service II Live Load (LL+IM), as computed by line-girder analysis Effective Slab Width Variation Along the Span. The effec- tive slab width values were computed along the span using (OPIS) and FEM, for comparable right and skewed configu- the proposed definition for positive moment section. The rations. As shown in the table, the line girder analysis signif- results are summarized in Table 6. Figures 36 and 37 illus- icantly overestimated the girder flange stresses in the skewed trate the effective slab width ratio variation (beff /b) and asso- bridges. This overestimation provided a source of conser- ciated bending moment diagrams versus normalized span vatism in the very situations where a full effective width was length (x /L) for simple-span bridges for interior and exterior not attained. girders, respectively. The values were determined based on For short-span skewed bridges, the computed effective the finite-element analysis results taken between a half width slab width ratios varied erratically along the span length. The on one side and the other half width on the other side of the effective slab width ratios at midspan of these short-span girder (interior) or the overhang width (exterior). The ending skewed bridges, the SS-19 and SS-21 bridges, were 0.90 and moments were calculated from element stresses and cross- 0.93, respectively. These short bridges also had their flange sectional area. The circles on the plots represent the data points sizes governed by the minimum flange size guideline rather

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29 Figure 32. HL-93 truck configurations, simple span, interior girder, positive moment. than by Service II or Strength I, as documented further in II effective widths, as expected. Representative results of this Appendix H. nature are provided in Appendix G. For exterior girders, all four skewed bridges experienced the effective slab width slightly smaller than the full width (see Figure 37). Of these, however, SS-25 had the highest 2.4.3 Continuous Span Bridges effective slab width ratio as expected because of flexural dominated behavior. A total of 16 multiple-span continuous bridges, providing The results presented here are for Service II conditions. At 64 subcases, were analyzed using ABAQUS. All these bridges Strength I loading levels, effective widths were always found are composed of four three-span continuous steel girders with from the FEM results to be equal or greater than the Service conventional reinforced concrete slab. Bridge configurations

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30 Figure 33. HL-93 truck configurations, simple span, exterior girder, positive moment. are summarized in Table 4 with four different parameters-- Negative Moment, Interior girder; and girder spacing (S), exterior span length (L1), interior-to- Negative Moment, Exterior girder. exterior span ratio (L2 /L1), and skew angle of the support (). Parameters range from 2.4 m to 4.8 m for girder spacing, 20 For the positive moment loading, the truck middle axles m to 60 m for exterior span length, 1.0 to 1.5 for interior-to- were placed at 0.4L1 where L1 was the exterior span length, exterior span ratio, and 0 deg to 60 deg for skew angle. Each with the rear axle facing the closest abutment (see Figures 38 bridge analysis consisted of four subcases at the Service II through 41). Lane load for the positive moment loading cases limit state: was applied only on the exterior span where the trucks were located. In addition, selected bridges were loaded in the mid- Positive Moment, Interior girder; dle span only and subjected to the truck loading at 0.5L2 Positive Moment, Exterior girder; where L2 was the interior span length. This was to simulate

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31 Figure 34. Lane load configurations, simple span, interior girder, positive moment. the positive moment condition on Span 2. These cases were Truck configurations are illustrated in Figures 42 to 45. Sim- used for validating the results obtained by loading on Span 1. ilarly, lane load was applied on both spans where the trucks For the negative moment loading, two truck middle axles were located, that is Spans 1 and 2. were placed on the exterior span at 0.6L1 and the other two truck middle axles were placed at 1.4L2, where L1 and L2 were the exterior and interior span lengths, respectively. These 2.4.3.1 Positive Moment Section locations were systematically chosen based on influence line concepts to maximize the negative bending moment at the Effective Slab Width Variation Along the Span. For posi- interior support. All trucks' rear axles were facing the clos- tive moment loading on the exterior span (Span 1), some sec- est abutment as described for the positive moment loading. tions along the bridge experienced negative bending moment,

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Figure 35. Lane load configurations, simple span, exterior girder, positive moment. TABLE 6 Effective slab width ratio ( beff /b) for simple-span bridges Bridge Interior Girder Exterior Girder ID 0.40L 0.45 L 0.50 L 0.55 L 0.60 L 0.40 L 0.45 L 0.50 L 0.55 L 0.60 L SS-01 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 SS-03 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 SS-07 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 SS-09 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 SS-14 1.00 1.00 1.00 1.00 1.00 0.98 0.97 0.95 0.97 0.98 SS-19 1.00 0.80 0.90 0.84 0.88 0.83 0.89 0.88 0.86 0.85 SS-21 0.85 0.80 0.93 0.81 0.81 0.80 0.75 0.80 0.78 0.78 SS-25 1.00 1.00 1.00 1.00 1.00 0.93 0.96 0.96 0.95 0.93 SS-27 0.95 0.92 0.94 0.94 0.94 0.80 0.81 0.92 0.83 0.80

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33 Figure 36. beff /b and bending moment versus x/L, simple span, interior girder, positive moment.

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Figure 37. beff /b and bending moment versus x/L, simple span, exterior girder, positive moment.

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35 TABLE 7 Comparison of 1.3(LL+IM) stresses in the bottom flange at 0.5L Bridge L (m) S (m) Flange Stress in RF Flange Stress OPIS (MPa) in FEM (MPa) SS-01 15 2.4 0 180.3 1.116 150 SS-09 60 4.8 0 86.8 1.423 60 SS-19 15 2.4 60 164.4 1.089 71 SS-27 60 4.8 60 93.23 1.171 48 especially the region near the interior pier. Hence, the effec- in Figures 46 and 47 for the interior girder of right and tive slab width values were computed based on the proposed skewed bridges, respectively. Similar plots for the exterior definitions for the positive and negative moments accordingly. girders are illustrated in Figures 48 and 49. The associated In this section, the main focus will be on the positive moment bending moment diagrams are plotted. Numerical results are section where the maximum positive bending moments take summarized in Table 8. place. The variations of effective slab width ratio were plot- All right bridge results indicate that the full width can be ted along the normalized span length between 0L1 and 1.1L2 used as the effective slab width for the critical positive moment Figure 38. HL-93 truck configurations of the multiple-span continuous cases (right bridges, interior girder, positive moment).

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36 Figure 39. HL-93 truck configurations of the multiple-span continuous cases (skewed bridges, interior girder, positive moment). section, at approximately 0.4L1 (see Figure 46). The reduction the interior span to the live load that maximizes the positive of the effective slab width occurs at the point of contraflexure bending moment of the interior girder. Figure 50 illustrates the where the transition of bending moment from positive to neg- effective slab width ratio variation along the normalized span ative takes place. This phenomenon will be addressed more length of all eight of these cases, i.e. CS-03, CS-07, CS-21, fully in the negative moment section discussion. CS-25, CS-57, CS-61, CS-75 and CS-79. These cases were The variations of effective slab width ratio for the highly chosen to ensure all the extreme cases in terms of L1/S were skewed bridges were rather chaotic. However, the effective covered. All bridges experienced a full width as the effective slab width value associated with the maximum positive slab width for positive moment in the middle span, except for moment section was relatively close to 1.0. The exterior gird- CS-75. The result was very consistent with the exterior span ers had more or less the same behavior as the interior girders loading case (see Figure G.48). in terms of effective slab width ratio (see Figures 48 and 49). Bridge CS-75, like SS-19 and SS-21, had not only high The case of loading on the interior span (Span 2) was also skew but also short spans such that the flange sizes in the pos- investigated. Eight selected cases were analyzed by subjecting itive moment region were governed by the minimum flange

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37 Figure 40. HL-93 truck configurations of the multiple-span continuous cases (right bridges, exterior girder, positive moment). size guideline rather than by Service II or Strength I, as doc- the effective slab width. The sole exception was the CS-03 umented further in Appendix H. bridge. For skewed bridges, a few cases had the effective slab width smaller than 1.0. In addition, the bending moment dia- grams associated with these skewed bridges deviated from 2.4.3.2 Negative Moment Section the line-girder analysis results as with skewed simple-span bridges. Moments extracted from FEM in such cases were This section focuses on the region close to the interior pier considerably less than those obtained from line-girder analy- where the negative moment is maximized. Many issues arise sis. The location of truck placement could have had a major under the investigation of the negative moment section and influence on the computed effective slab width ratios, espe- will be explored more fully as the discussion progresses. cially in the short and high skewed bridge (see Figure 52). Effective Slab Width Variation Along the Span. Figures 51 Similar plots of the exterior girder are illustrated in Figures and 52 demonstrate how the effective slab width ratios of the 53 and 54. All exterior girder cases, except the CS-03 bridge, interior girder varied in the region close to the interior pier, experienced a full width as the effective slab width. Numer- 1.0L1. Almost every right bridge experienced full width as ical results are summarized in Table 9.

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38 Figure 41. HL-93 truck configurations of the multiple-span continuous cases (skewed bridges, exterior girder, positive moment). Uncracked Versus Cracked Sections. From the result of tive slab width. As soon as the entire slab reaches the con- the investigation using the new effective slab width defini- crete tensile strength, the slab becomes a cracked section. tion for the negative moment section, the concrete slab can Forces start to transfer from slab to rebars, which pushes the be divided into two categories: uncracked and cracked. There effective slab width wider until the full slab width is reached. are major distinctions between the two slab types, which in As for the positive moment region, the results presented turn affect how much of the slab contributes to resisting ten- here are for Service II conditions. At Strength I loading lev- sile stresses. els, effective widths were always found from the FEM results An uncracked slab section is an intact condition of the to be equal to or greater than the Service II effective widths, concrete slab that is subjected to tensile stresses below the as expected. Representative results of this are provided in concrete tensile strength. Both concrete and rebars are work- Appendix G. ing together and sharing tensile forces accordingly. At low stress levels, this gives a smaller effective slab width. Once 2.4.4 Summary of FEM Parametric Study cracks initiate, tensile stresses would be redistributed in the uncracked portion of the slab and result in the larger effec- FEM results showed the following: